Gravitational wave astronomy has now left its infancy and has become an important tool for probing the most violent phenomena in our universe. The LIGO/Virgo-KAGRA collaboration operates ground based detectors which cover the frequency band from 10 Hz to the kHz regime, meanwhile the pulsar timing array and the soon to launch LISA mission will cover frequencies below 0.1 Hz, leaving a gap in detectable gravitational wave frequencies. Here we show how a Laser Interferometer On the mooN (LION) gravitational wave detector would be sensitive to frequencies from sub Hz to kHz. We find that the sensitivity curve is such that LION can measure compact binaries with masses between 10 and 100M at cosmological distances, with redshifts as high as z= 100 and beyond, depending on the spin and the mass ratio of the binaries. LION can detect binaries of compact objects with higher-masses, with very large signal-to-noise ratios, help us tounderstand how supermassive black holes got their colossal masses on the cosmological landscape, and it can observe in detail intermediate-mass ratio inspirals at distances as large as at least 100 Gpc. Compact binaries that never reach the LIGO/Virgo sensitivity band can spend significantamounts of time in the LION band, while sources present in the LISA band can be picked up by the detector and observed until their final merger. Since LION covers the deci-Hertz regime with such large signal-to-noise ratios, it truly achieves the dream of multi messenger astronomy
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